#### Vol. 12, No. 4, 2017

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1559-3959 Author Index To Appear Other MSP Journals
Highly accurate noncompatible generalized mixed finite element method for 3D elasticity problems

### Guanghui Qing, Junhui Mao and Yanhong Liu

Vol. 12 (2017), No. 4, 505–519
##### Abstract

Based on the generalized H–R mixed variational principle, the simple compatible and noncompatible generalized mixed elements (CGME, NCGME) for 3D linear elasticity problems were derived by the ${C}_{0}$ continuous polynomial shape functions used usually in the displacement methods. Two of main features of the generalized mixed finite element methods corresponding to the CGME and NCGME are that the coefficient matrix of system of equations are automatically symmetric and invertible. Without any extra techniques of the traditional mixed methods, the displacement and stress results can be obtained directly from the linear system of equations by introducing the stress and displacement boundary conditions simultaneously. The numerical examples show that the displacement and stress variables converge stably. The resulting stresses of NCGME have nearly the same accuracy as displacements and are certainly more accurate than the common noncompatible displacement finite element methods.

##### Keywords
H-R mixed variational principle, mixed element, generalized H-R mixed variational principle, compatible generalized mixed element, noncompatible generalized mixed element
##### Milestones
Received: 2 February 2017
Revised: 20 March 2017
Accepted: 25 April 2017
Published: 28 June 2017
##### Authors
 Guanghui Qing College of Aeronautical Engineering Civil Aviation University of China Jinbei Road 2898 Tianjin, 300300 China Junhui Mao College of Aeronautical Engineering Civil Aviation University of China Jinbei Road 2898 Tianjin, 300300 China Yanhong Liu College of Aeronautical Engineering Civil Aviation University of China Jinbei Road 2898 Tianjin, 300300 China